How to trigger LMB click events to activate a specific View node and update contents of 'Viewer Node' image data block using Python?
Very good question. But The answer at this moment is you can’t. The python interpreter needs to be finished in order to start the compositor recalculation. This is a background job and after it is finished you know for certain that the new image has been updated.

If we would have a possibility in the API to find out if the background job of the compositor is running we would be able to start a python thread or modal window to wait for this to happen and then continue the task you want to do.

Perhaps best solution ATM is to use the file output node to always store those all outputs and when needed read them back.